Bücher von Farida Khursheed

Doctoral Thesis / Dissertation from the year 2015 in the subject Mathematics - Applied Mathematics, , language: English, abstract: This book comprises various optimality criteria, duality and mixed duality in a variety of mathematical programming, that includes nondifferentiable nonlinear programming problems, nondifferentiable nonlinear fractional programming problems, nondifferentiable minimax fractional programming problems etc.Mathematical Programming is concerned with the determination of a minimum or maximum of a function of several variables, which are required to satisfy a number of constraints. Such solutions are sought are sought in diverse fields, including Engineering, Operations Research, Management Science and Economics. Often these situations are mathematical representations of certain real world problems, and hence are turned as mathematical programming problems.Optimality criteria and duality have played an important role in the development of mathematical programming. Optimality conditions were first investigated by Fritz John and later on, independently by Karush and Kuhn ¿ Tucker. The inception of duality theory in linear programming may be traced to the classical minmax theorem of Von Neumann, which was subsequently formulated in a precise form by Gale, Kuhn and Tucker. Since then optimality criteria and duality have remained as one of the most widely investigated area in mathematical programming. Karush-Kuhn-Tucker conditions not only laid down the foundations for many computational techniques in mathematical programming, but also are a great deal responsible for the development of the duality theory.An extensive use of duality in mathematical programming has been made for many theoretical and computational developments in mathematical programming itself, economics, control theory, business problems and many other diverse fields. It is well known that duality principle connects two programs, one of which, called the Primal problem, is a constrained maximization (or minimization) problem, and the other one called the Dual, is a constrained minimization (or maximization) problem, in such a way that the existence of an optimal solution to one of them guarantees an optimal solution to the other and optimal values of the two problems are equal. A pair of dual problems is called symmetric if the dual of the dual is the primal itself.

With the improvement in cryptanalysis techniques, need of more secure techniques evolved. Accordingly, people thought of using covers for hiding the sensitive information. This hiding of information in covers is known as Steganography. In Steganography that uses images as covers, main goal is to embed information in such a way so as to make information imperceptible. A number of techniques were developed to embed the information in spatial and frequency domain .For embedding of information in transform domain the images are first transformed to frequency domain to save it from Common cover attacks. However, transformation of image into frequency domain for embedding and then retrieval of information is computationally expens¿ve. In this work, therefore, attempt has been made to embed the information in fuzzy logic domain. Results reveal the advantages of embedding not only in terms of computational ease but it also in terms of embedding versatility; since it embeds text, color and grey level images with higher payload and imperceptibility.

From security point of view, identity of a person is of critical importance. Increased threats to conventional security methods of personal identification has given rise to personal identification and verification systems based on biometrics. These systems establish human identity using individual¿s physical or behavioral attributes. These attributes besides being universal, unique and permanent need to be acceptable as well. One such biometric modality that has potential for further exploration is Ear. As a step in this direction, we have made an attempt to explore the potential of time series based Autoregressive (AR) modelling. Performance of AR model using ear biometrics motivated us to make an attempt for 100% RR of a person based on multimodal biometrics. After a study of state of art biometric modalities and potential of second order texture based methods having capability to extract information beyond visual perception, we found it reasonable to fuse AR based feature vector of Ear shape with second order texture based statistics of biometric modality Iris.